Effect of Rare Earth La–Ce on Solidification Structure of 3.2%Si-0.9%Al Non-oriented Silicon Steel

Abstract

The effect of rare earth on the solidification structure of 3.2%Si-0.9%Al non-oriented silicon steel was investigated using industrial trials. The outputs demonstrated that increasing rare earth content leads to a decrease in the average size of equiaxed crystals in the casting billets. In order to further understand the rare earth on the grain refinement of δ-ferrite, the conventional inclusion detection technology, was used to investigate the distribution characteristics of inclusions, together with theoretical calculation of the equilibrium partition coefficients, pinning forces and mismatch degrees. The detection results of inclusions and the calculation results of pinning force showed that the effect of rare earth on the pinning force of inclusions was marginal. Thermodynamic calculation indicated that Ce addition had negligible effect on the equilibrium partition coefficient of Si, Al and Mn. Combined with the calculation results of GRF model, it is reasonable to consider that the contribution of rare earth element to the refinement of equiaxed crystals can be ignored. Further, the outcomes obtained from the E2EM model calculations revealed that the principal mechanism responsible for the refinement of equiaxed crystals through rare earth treatment can be attributed to the heterogeneous nucleation effect of (La, Ce)₂O₂S.

1. Introduction

The content of Si+Al in high-grade non-oriented silicon steel ranges from 1.5% to 4.0%. It is mainly used in the manufacturing of large and medium-sized motors.^1,2,3) Utilizing non-oriented silicon steel with excellent magnetic properties can enhance energy utilization efficiency, reduce motor size, and improve motor lifespan.⁴⁾ The primary factors that affect the magnetic properties of non-oriented silicon steel include composition^5,6)texture,^4,7) non-metallic inclusions,^8,9) and final grain size.¹⁰⁾

The application of rare earth treatment is an important method for reducing the detrimental effects of inclusions and controlling the grain size of non-oriented silicon steel.^11,12) Optimal grain size of the final product can be achieved by adding an appropriate amount of rare earth elements, thus enhancing the magnetic properties of non-oriented silicon steel.¹³⁾ The grain size of the final product in non-oriented silicon steel is closely linked to the grain size of the casting billet due to the hereditary nature of the microstructure.^14,15) Previous studies have demonstrated that rare earth treatment of the casting billet results in notable grain refinement in the equiaxed grain,^{16,17,18,19,20,21,22,23,24)} and an increase in the proportion of equiaxed grains has been observed in certain studies.^25,26,27,28) The refinement of the solidification structure through rare earth treatment can be primarily attributed to three mechanisms. One mechanism is the heterogeneous nucleation effect of rare earth inclusions,^16,18,23) where rare earth inclusions act as heterogeneous nucleation sites, promoting the formation and refinement of equiaxed grains. The other mechanism is the solute effect of rare earth atom,²⁶⁾ where the segregation of rare earth atoms at the solid-liquid interface suppresses grain growth, resulting in the refinement of the solidification structure. In addition, fine inclusions can pin grain boundaries and hinder the growth of equiaxed grains in billets. The impact of rare earth treatment on the average size of equiaxed grains within billets was mediated by its influence on the type, morphology, and size of inclusions.^29,30)

Currently, research findings have not conclusively revealed the primary mechanism responsible for the refinement of billet solidification microstructure through rare earth treatment. In addition, there is a lack of application results from industrial-scale tests, and it is essential to consider that the process route of industrial production for non-oriented silicon steel differs significantly from laboratory conditions. The industrial production process involves complex factors that can influence the performance and effects of rare earth addition in a different manner compared to controlled laboratory settings. Accordingly, this study undertakes an industrial-scale investigation into rare earth treatment effects on the solidification microstructure of non-oriented silicon steel billets, encompassing a carefully selected range of rare earth content. By integrating analyses of inclusions, billet microstructure, and theoretical computation, this research comprehensively explores the influence of composite rare earth treatment on the solidification microstructure of non-oriented silicon steel billets.

2. Materials and Analysis Methods

2.1. Materials

The industrial experiment was conducted at a steel plant to investigate the influence of rare earth treatment on the solidification microstructure of non-oriented silicon steel. The production process for non-oriented silicon steel involved converter refining, RH refining, continuous casting, hot rolling, normalizing, cold rolling, and annealing. Table 1 presents the chemical compositions of the four heats of molten steel. The alloying elements, as well as the aluminum and silicon content, remained essentially the same across the four heats. The La+Ce content in Table 1 was determined by ICP-MS analysis.

Table 1. The Chemical composition of the four heats of molten steel (wt%).

Heat	C	Mn	S	P	Si	Als	N	La+Ce
1	0.0024	0.27	0.0021	0.012	3.21	0.89	0.0020	0
2	0.0023	0.28	0.0019	0.013	3.20	0.91	0.0021	0.0021
3	0.0024	0.29	0.0020	0.015	3.18	0.87	0.0020	0.0034
4	0.0021	0.27	0.0020	0.012	3.20	0.90	0.0020	0.0058

2.2. Methods

Sampling was performed during the continuous casting and hot rolling stages of the industrial experimental process. Figure 1 illustrates the process of preparing specimens from the casting billet. A metallographic sample was taken from the casting billet, with dimensions of 15 mm × 15 mm × 15 mm. For the hot-rolled plate, sampling was performed immediately after the completion of the hot rolling process, and specimens with dimensions of 8 mm (transverse direction) × 10 mm (rolling direction) were prepared using a wire cutter.

Fig. 1. The preparation process for the casting billet specimen. (Online version in color.)

Following the preparation of the casting billet specimens through grinding and polishing, a qualitative analysis of typical inclusions within the samples was performed using the JSM-6490LV scanning electron microscope, which was equipped with an energy-dispersive X-ray spectroscopy (EDS) system. The ASPEX Inclusion Analysis System was utilized for the quantitative analysis of typical inclusions in both the casting billet and hot-rolled plate specimens. During the detection process, the ASPEX inclusion scanning device maintains a fixed magnification of 4000 times and scans an area of 20 mm². A metallographic sample was cut from the middle portion of the billet and subjected to mechanical grinding, polishing, and etching with a hydrochloric acid solution. Subsequently, the low-magnification structure of the casting billet was captured using a high-resolution Nikon digital camera. The average diameter of ferritic grains within the solidification structure of the billet treated with various rare earth contents was then determined using the metal average grain size measurement method prescribed by the national standard GB-T 6394-2002.

3. Results

3.1. Characterization of Solidification Structure

In the current industrial experiment, non-oriented silicon steel with a silicon (Si) content of 3.2 wt% was manufactured. Based on the Fe–Si phase diagram, the solidification microstructure of the casting billet, treated with different rare earth contents, was believed to consist of a single-phase ferrite structure. This ferrite structure remains stable throughout the cooling process of the molten steel. Thus, in this experiment, studying the refinement mechanism of the solidification microstructure under rare earth treatment can avoid interference caused by solid-state phase transformations.

Figure 2 illustrates the macroscopic solidification microstructure of the casting billet after being treated with different rare earth contents. It can be observed that the solidification microstructure includes a fine-grained region on the surface, a columnar crystal region, and an equiaxed crystal region at the center. The overall microstructure consists of a single ferrite phase.

Fig. 2. The macroscopic solidification microstructure after being treatment with different rare earth contents (a) 0 wt% (b) 0.0021 wt% (c) 0.0034 wt% (d) 0.0058 wt%. (Online version in color.)

Figure 3 illustrates the average grain diameter of equiaxed crystals in the solidification structure, which is treated with various concentrations of rare earth elements. Moreover, it was revealed that the average width and rate of columnar crystals change with the increase of rare earth content. The statistical results demonstrated that the average grain diameter of the equiaxed crystals gradually decreases as the rare earth content increases from 0 wt% to 0.0058 wt%. In the untreated casting billet, the average grain size of the equiaxed crystals was 3.5 mm. However, with a rare earth content of 0.0058 wt%, the average grain size of the equiaxed crystals in the solidification microstructure decreases to 2.4 mm, indicating a refinement rate of 31.43% compared to the solidification microstructure achieved through conventional treatment. Consequently, the rare earth treatment leads to a significant refinement effect in the solidification microstructure.

Fig. 3. Variation trend of equiaxed crystal average size, columnar crystal average width and columnar crystal rate with the increase of rare earth content. (Online version in color.)

The results of this experiment indicated that rare earth treatment has minimal effect on the columnar crystal fraction of the solidification microstructure. The columnar crystal fraction shows minimal overall fluctuations, ranging from 37% to 38% for different rare earth contents. The columnar crystal fraction of the casting billet in practical industrial production of non-oriented silicon steel was mainly influenced by continuous casting process parameters, such as casting speed. Therefore, based on this experiment, it can be concluded that rare earth treatment has a minimal effect on the columnar crystal fraction of the solidification microstructure. The impact of rare earth on the columnar crystal rate in the solidification structure might be relatively small, but this doesn’t imply that rare earth has no effect on the growth of columnar crystals. To illustrate this point, we further analyzed the influence of different rare earth contents on the average width of columnar crystals. It is evident that with an increase in rare earth content, the average width of columnar crystals decreases. This indicates that rare earth does have some influence on columnar crystals, but the specific effects and mechanisms of rare earth on the growth of columnar crystals still require further research.

3.2. Distribution Characteristics of Typical Inclusions in Casting Billet

Figure 4(a) illustrates the types and morphologies of typical inclusions in the casting billet under conventional processing. In the casting billet without rare earth treatment, the inclusions primarily consist of composite inclusions formed between oxides (MgO, Al₂O₃, CaO) and sulfides (CaS), along with a portion of AlN inclusions. Among them, the composite inclusions predominantly exhibit spherical or near-spherical shapes, such as MgO–Al₂O₃–CaO–CaS and MgO–Al₂O₃–CaO, whereas the AlN inclusions exhibit irregular square shape.

Fig. 4. Types and morphologies of typical inclusions in casting billets with different rare earth contents (a) 0 wt% (b) 0.0021 wt% (c) 0.0034 wt% (d) 0.0058 wt%. (Online version in color.)

The introduction of a certain amount of rare earth alloy during the industrial experimental process leads to significant changes in the types of inclusions within the casting billet. Moreover, variations in the types of inclusions are observed in specimens with different levels of rare earth content. Based on the scanning results shown in Fig. 4(b), the primary inclusions in the casting billets treated with 0.0021 wt% La+Ce composite rare earths consist of composite inclusions, namely (La, Ce)AlO₃-AlN. The composite inclusion consists of a (La, Ce)AlO₃ core, while the outer layer comprises AlN precipitated during the cooling process. Furthermore, partial (La, Ce)AlO₃-(La, Ce)₂O₂S-AlN composite inclusions are detected. Figure 4(c) shows the morphology types of typical inclusions in the casting billet treated with 0.0034 wt% rare earth, with the main type of inclusion being (La, Ce)AlO₃-(La, Ce)₂O₂S-AlN. Figure 4(d) presents the morphology types of typical inclusions in the casting billet treated with 0.0058 wt% rare earth. The results indicated the presence of (La, Ce)₂O₂S-AlN composite inclusions as well as independently observed (La, Ce)₂O₂S inclusions in the specimen. Based on the comprehensive analysis of the aforementioned detection results, it can be concluded that an increase in rare earth content leads to a gradual transition of the primary type of rare earth inclusion from (La, Ce)AlO₃ to (La, Ce)₂O₂S.

The ASPEX Inclusion Analysis System was used to collect statistical data on the changing trends of rare earth inclusions in both the casting billet and hot-rolled microstructures. The statistical results, shown in Fig. 5, reveal that at a rare earth content of 0.0021 wt%, the number density of rare earth inclusions in the casting billet and hot-rolled microstructures were 1.8#/mm² and 7.25#/mm², respectively. With an increase in the added rare earth content to 0.0058 wt%, the number density of rare earth inclusions in the casting billet and hot-rolled microstructures rises to 4.75#/mm² and 11.75#/mm², respectively. Consequently, the number density of rare earth inclusions in both the casting billet and hot-rolled microstructures demonstrates a steady increase as the rare earth content increases. Specifically, at a rare earth content of 0.0021 wt%, the number density of (La, Ce)AlO₃ inclusions was 1.7#/mm² in the casting billet and 6.5#/mm² in the hot-rolled microstructures, while the number density of (La, Ce)₂O₂S inclusions was 0.1#/mm² and 0.75#/mm², respectively. As the rare earth content was raised to 0.0058 wt%, the number density of (La, Ce)AlO₃ inclusions in the casting billet and hot-rolled microstructures decreases to 0.25#/mm² and 0.75#/mm², respectively, whereas the number density of (La, Ce)₂O₂S inclusions increases to 4.5#/mm² and 11#/mm², respectively.

Fig. 5. The changing trend of number density of rare earth inclusions with the increase of rare earth content. (Online version in color.)

In summary, as the rare earth content increases, the stability of (La, Ce)₂O₂S inclusions strengthens in both the casting billet and hot-rolled microstructures. The primary type of rare earth inclusion gradually shifts from (La, Ce)AlO₃ to (La, Ce)₂O₂S, and the content of (La, Ce)₂O₂S in the specimens continues to rise.

4. Discussions

4.1. Solute Effect of Rare Earth Elements

The phenomenon of grain refinement due to solute is frequently denoted as the growth restriction effect of solute. This phenomenon arises from the enrichment or depletion of solute species ahead of the solid-liquid interface. Solute segregation during solidification results in the formation of a zone known as constitutional supercooling (CS) at the solid-liquid interface. When the combined influence of thermal undercooling and constitutional supercooling surpasses the critical supercooling threshold for nucleation, it promotes the formation of additional nuclei within the constitutional supercooling zone, ultimately contributing to grain refinement during the solidification process.³¹⁾ The equilibrium partition coefficient strongly influences solute partitioning. Hence, an investigation was conducted to assess the impact of introducing rare earth elements on the equilibrium partition coefficient of individual elements. The equilibrium distribution coefficient for a solute, as represented by Eq. (1), is defined as the ratio of solute concentration at the solid-liquid interface in the solid phase to that in the liquid phase.

  

$$k_i=\frac{c_i^s}{c_i^L}$$(1)

Within the equation, k_i represents the equilibrium distribution coefficient of solute i; $c_i^S$ and $c_i^L$ denote the equilibrium concentrations of solute i in the solid phase at the solidification front and in the liquid phase, correspondingly. In this study, the equilibrium concentrations of solutes during the solidification process were determined using the equlib module of Factsage8.2. The equilibrium distribution coefficients of the solutes were then determined using Eq. (1). For simplicity, the equilibrium distribution coefficients were calculated using the Fe-3.2wt%Si-0.90wt%Al-0.28wt%Mn-Ce systems. Figure 6 display the calculated equilibrium distribution coefficients of Si, Ce, Al and Mn in the Fe-3.2wt%Si-0.90wt%Al-0.28wt%Mn-Ce system throughout the solidification process, considering different Ce contents. Figure 6(a) presents the calculated equilibrium distribution coefficients of Si in the Fe-3.2wt%Si-0.90wt%Al-0.28wt%Mn-Ce system at different temperatures during solidification, considering various Ce contents. The equilibrium partition coefficients of Si exhibit an initial increase followed by a decrease with decreasing solidification temperature. However, the impact of Ce content on the equilibrium partition coefficients of Si was marginal, despite a slightly lower value observed at higher Ce concentrations. Thermodynamic calculations indicated that the addition of Ce results in decreased solute concentrations of Si in the solid phase and increased concentrations in the liquid phase at equilibrium for all calculated temperatures. Consequently, the addition of Ce leads to a marginal decrease in the equilibrium partition coefficients of Si, as illustrated in Fig. 6(a). Figure 6(b) demonstrates that the equilibrium distribution coefficient of Ce initially decreases and then increases as the solidification temperature decreases. Under identical solidification temperatures, an increase in Ce content results in a slight rise in the calculated equilibrium partition coefficients of Ce. Such increase was attributed to the decrease in Ce concentration in the liquid as more Ce was added, but the Ce solid solubility increases slightly.

Fig. 6. Equilibrium distribution coefficients of elements in Fe-3.2wt%Si-0.90wt%Al-0.28wt%Mn-Ce system during solidification under different Ce contents (a) Si (b) Ce (c) Al (d) Mn. (Online version in color.)

Figures 6(c) and 6(d) illustrate the trends in equilibrium distribution coefficients for Al and Mn as the Ce content varies within the system. It can be observed that the influence of adding Ce on the equilibrium distribution coefficients of Al and Mn can be neglected within the range of Ce content from 0 wt% to 0.1 wt% in the system. In conclusion, the impact of Ce addition on the equilibrium distribution coefficients of Si, Al, and Mn in this system is negligible within the specified range of Ce content, specifically 0 wt% to 0.1 wt%.

The growth restriction factor (GRF) model was employed for a quantitative analysis of how solute effects, specifically those from rare earth elements, impact the refinement of the solidification structure in non-oriented silicon steel.^32,33) The letter Q represents the Growth Restriction Factor, where a higher Q value signifies a more pronounced growth restriction effect of the solute.³¹⁾ The mathematical formula for calculating the Q value, as outlined in reference,³⁴⁾ is presented in Eq. (2) below.

  

$$Q=m{C}_0(k-1)$$(2)

In the equation, m represents the slope of the liquidus line in the binary phase diagram, given in units of k/(wt.%), C₀ represents the concentration of the solute element in percentage (%), and k denotes the equilibrium distribution coefficient of the solute element.

Binary phase diagrams for Fe–Si, Fe–Ce, Fe–La, Fe–Al, and Fe–Mn were generated using the Phase Diagram module of Factsage 8.2 software. Parameters m and k were derived from these diagrams, and formula (2) was employed to calculate the Q value. The calculation process overlooked the impact of rare earth addition on the equilibrium distribution coefficients of solute elements Si, Al, and Mn.

Figure 7 illustrates the variation in calculated Q values for La and Ce as a function of rare earth element content. The results in Fig. 7 indicate a rising trend in Q value as the content of La and Ce increases. For higher concentrations of rare earth elements, the Q value for La was slightly higher than that for Ce. In the current industrial experiment, the maximum rare earth element content added was 0.0058 wt%, leading to Q values of 0.04568 for La and 0.04409 for Ce, respectively. However, as per the formula, the calculated Q value for 3.2 wt% Si was 14.409, for 0.90 wt% Al it was 0.6056, and for 0.28 wt% Mn, it was 0.4217. This meant that the contribution of the solute of Ce to the overall Q value is very marginal, which implies the negligible contribution of Ce to the grain refinement as a solute.

Fig. 7. Calculated Q values of La and Ce with different rare earth content. (Online version in color.)

4.2. Pinning Effect of Inclusions after Rare Earth Treatment

Within non-oriented silicon steel, the notable thermal stability of small non-metallic inclusions results in their ability to exert pinning or drag effects on grain boundaries.³⁵⁾ Gladman³⁶⁾ proposed that a decrease in grain boundary interfacial energy stimulates grain growth, and he elucidated the connection between grain boundary interfacial energy and the driving force for grain growth, as represented in Eq. (3). Zener et al.³⁷⁾ introduced a formula for calculating the pinning force, which is expressed by the specific equation presented in Eq. (4).

  

$$F_{\text{d}}=\left(\frac{3}{2}-\frac{2}{Z}\right)\left(\frac{\gamma }{R}\right)$$(3)

  

$$F_{Zener}=\left(\frac{3}{2}\right)\left(\frac{\sigma \cdot f}{D}\right)$$(4)

In the equation, γ and σ represent the grain boundary energy per unit area (typically assumed as 0.8 J/m²); R is the average grain size (μm); Z stands for the second phase size inhomogeneity factor (in this context, the ratio of the maximum size of the second phase to the average size), f denotes the volume fraction of the second phase, and D represents the size of the second phase.

As previously mentioned, rare earth treatment primarily affects the distribution of Al₂O₃, MnS, and rare earth inclusions in non-oriented silicon steel. To investigate the pinning effect of inclusions on the equiaxed crystals in the billet after rare earth treatment, the distribution patterns of second-phase inclusions with sizes ranging from 300 to 500 nm, 500 to 1000 nm, 1000 to 3000 nm, and 3000 to 5000 nm were separately analyzed. The pinning forces of Al₂O₃, MnS, and rare earth inclusions on grain growth were computed for different size ranges, as presented in Table 2 and depicted in Fig. 8.

Table 2. Distribution density of Al₂O₃, MnS and rare earth inclusions, along with calculated pinning forces on grain growth.

Inclusion	Size Range, nm	Distribution Density, Per cm3				Fzener, Pa
		0 ppm	21 ppm	34 ppm	58 ppm	0 ppm	21 ppm	34 ppm	58 ppm
Al2O3	300–500	4.41E+07	1.83E+07	1.38E+07	2.69E+07	5.36	2.22	1.69	3.24
	500–1000	2.35E+07	1.07E+07	9.91E+06	1.39E+07	7.00	3.52	4.10	5.60
	1000–3000	7.23E+06	2.75E+06	4.85E+06	5.33E+06	14.67	8.98	12.50	13.75
	3000–5000	5.57E+05	6.16E+05	2.62E+05	3.35E+05	5.70	7.54	2.72	2.89
MnS	300–500	3.14E+07	1.41E+07	1.33E+07	6.18E+06	3.27	1.68	1.40	0.75
	500–1000	6.90E+06	7.13E+06	5.69E+06	4.12E+06	2.52	2.33	1.95	1.67
	1000–3000	2.04E+06	1.31E+06	1.00E+06	6.85E+05	4.01	3.09	2.39	1.55
	3000–5000	1.92E+05	2.54E+05	1.91E+05	1.38E+05	1.65	2.80	1.65	1.60
Re-inclusions	300–500	/	7.51E+05	1.05E+06	2.25E+06	/	0.07	0.10	0.22
	500–1000	/	3.02E+05	4.99E+05	1.15E+06	/	0.18	0.28	0.69
	1000–3000	/	5.69E+05	1.06E+06	1.43E+06	/	2.04	3.14	5.73
	3000–5000	/	1.04E+05	1.77E+05	2.07E+05	/	1.35	2.10	2.39
Total	/	1.16E+08	5.69E+07	5.18E+07	6.26E+07	44.18	35.8	34.02	40.08

Fig. 8. Ce–S equilibrium phase diagram calculated by Factsage8.2 software. (Online version in color.)

As shown in Table 2, it was evident that with the escalation of rare earth content, the distribution density of Al₂O₃ inclusions experiences an initial reduction followed by an increase. The distribution density of rare earth inclusions prominently increases, while the distribution density of MnS shows a decreasing trend. To further determine the variation patterns of inclusion, the Ce–S equilibrium phase diagram in the composition system of non-oriented silicon steel was computed using the Factsage 8.2 thermodynamic calculation software. During the computational process, owing to the similar nature of Ce and La, the thermal calculations were performed using the content of Ce as a surrogate for the composite rare earth content. The calculated results are depicted in Fig. 8. By integrating the detected inclusion results from different rare earth content in the billet and the Ce–S equilibrium phase diagram, it can be founded that with the increase in La+Ce content, the transition sequence of inclusions was Al₂O₃→(La,Ce)AlO₃→ (La,Ce)₂O₂S. The stable inclusion phases corresponding to rare earth contents of 0.0021 wt%, 0.0034 wt%, and 0.0058 wt% were CeAlO₃, a combination of CeAlO₃ and Ce₂O₂S, and Ce₂O₂S, respectively. At a composite rare earth content of 0.0021 wt%, the rare earth elements primarily give rise to rare earth inclusions of (La, Ce)AlO₃ type. These inclusions act as deoxidizing agents and modifiers, facilitating the transformation of Al₂O₃ inclusions. As the rare earth content in steel increases, the formation of rare earth inclusions transitions towards (La, Ce)AlO₃-(La, Ce)₂O₂S and (La, Ce)₂O₂S inclusions. These inclusions mitigate the formation of sulfides within the steel. However, their influence on the numerous Al₂O₃ inclusions formed during temperature drops and secondary oxidation was limited. As a result, this leads to a notable augmentation in the distribution density of Al₂O₃ inclusions within steel characterized by a substantial rare earth content.

Figure 9 illustrates that the pinning forces of Al₂O₃, MnS and rare earth inclusions to grain boundaries. It can be founded that the pinning force of Al₂O₃ inclusions on equiaxed crystal grains in the billet initially decreases and then increases with the increase in rare earth content. The pinning force of rare earth inclusions on equiaxed crystal grains rises with the augmentation of rare earth content. The pinning force of MnS on grain boundaries shows a decreasing trend with increasing rare earth content. Table 2 illustrates that the overall pinning force of inclusions in billets subjected to both rare earth treatment and conventional treatment falls within the 30–40 Pa range, with a subtle variation. In summary, the effect of rare earth treatment on the pinning force of inclusions can be ignored. It can be inferred that the pinning effect of inclusions was not the primary mechanism driving the refinement of billet solidification microstructure through rare earth treatment.

Fig. 9. The pinning forces of Al₂O₃, MnS and rare earth inclusions to grain boundaries (a) Al₂O₃ (b) MnS and rare earth inclusions. (Online version in color.)

4.3. Heterogeneous Nucleation Effect of Rare Earth Inclusions

The primary criterion for determining the effectiveness of inclusions as nucleating particles is whether their melting point exceeds that of the alloy. In the case of rare earth inclusions in steel, their melting points surpass the refining temperature of RH and continuous casting temperature. The inherent physical properties of rare earth inclusions in steel determine the fundamental conditions for their role as heterogeneous nucleation sites. The objective of this study is to explore the capability of high-melting-point rare earth inclusions as efficient heterogeneous nucleation centers for δ-Ferrite formation during steel solidification, with emphasis on a crystallographic viewpoint. In this study, the Edge-to-Edge Matching (E2EM) model was employed to assess the degree of matching between rare earth inclusions and δ-Ferrite. The E2EM model, initially introduced by Kelly et al.,³⁸⁾ represents an advanced crystallographic model that extends the two-dimensional misfit model. This model predicts the orientation relationship between crystal structures and has been validated for practical applications. The calculation formula for the E2EM model is as follows:³⁹⁾

  

$$f_{\mathrm{r}}=\frac{\left|r_{\mathrm{M}}-r_{\mathrm{P}}\right|}{r_{\text{P}}}$$(5)

  

$$f_{\text{d}}=\frac{\left|d_{\text{M}}-d_{\text{P}}\right|}{d_{\text{P}}}$$(6)

where f_r represents the lattice mismatch in atomic spacing, while f_d represents the lattice mismatch in interplanar spacing. r_M and r_P are the interatomic spacings along the matching directions in the matrix phase and the precipitate, respectively. The parameters d_M and d_P are the interplanar spacings of the matching planes in the matrix phase and the precipitate, respectively.

The crystallographic data necessary for E2EM model calculations was acquired through consultation of the Inorganic Crystal Structure Database (ICSD), utilization of the Findit software for crystallographic information, and referencing pertinent literature. The obtained information has been listed in Table 3.^{40,41,42,43,44)} It is worth noting that previous studies have confirmed a relatively small impact of lattice constant variation caused by thermal expansion on crystallographic calculations.^45,46) Therefore, during the calculation process of the E2EM model, the lattice constants of each phase at room temperature were employed, disregarding the influence of thermal expansion on these constants. Table 4 presents the atomic spacing mismatch between the rare earth inclusions and δ-Ferrite along the matching direction, as well as the face spacing mismatch along the matching planes, as calculated by the E2EM model.

Table 3. The crystal structures, space groups, and lattice parameters of δ-Ferrite and LaAlO₃, CeAlO₃, La₂SO₂, and Ce₂SO₂.

Phase	Structure	Space group	Lattice parameter/nm
δ-Fe	BCC	Im3m	a=0.2932
LaAlO3	Cubic	Pm3m	a=b=c=0.3791
CeAlO3	Cubic	Pm3m	a = b=c=0.3820
La2O2S	Hexagonal	P3m1	a=b=0.4049, c=0.6939
Ce2O2S	Hexagonal	P3m1	a=b=0.4001, c=0.6888

Table 4. The computed mismatch degrees between δ-Ferrite and LaAlO₃, CeAlO₃, La₂SO₂, and Ce₂SO₂.

Matching rows	Misfit (fr)/%	Matching type	Matching planes	Mismatch (fd)/%
$<100{>}_{\delta \text{-}\mathrm{F}\mathrm{e}}//<111{>}_{{\text{LaAlO}}_3}$	11.97	SS-SS	${\left\{110\right\}}_{\delta \text{-Fe}}//{\left\{111\right\}}_{{\text{LaAlO}}_3}$	5.60
$<100{>}_{\delta \text{-Fe}}//<111{>}_{{\text{CeAlO}}_3}$	12.82	SS-SS	${\left\{110\right\}}_{\delta \text{-Fe}}//{\left\{111\right\}}_{{\text{CeAlO}}_3}$	6.37
$<110{>}_{\delta \text{-Fe}}//<11\overline{2}0{>}_{{\text{La}}_{\text{2}}{\text{O}}_{\text{2}}\text{S}}$	2.34	SS-SS	${\left\{110\right\}}_{\delta \text{-Fe}}//{\left\{11\overline{2}0\right\}}_{{\text{La}}_{\text{2}}{\text{O}}_{\text{2}}\text{S}}$	2.32
$<100{>}_{\delta \text{-Fe}}//<\overline{1}101{>}_{{\text{La}}_{\text{2}}{\text{O}}_{\text{2}}\text{S}}$	9.17	SS-PS
$<110{>}_{\delta \text{-Fe}}//<11\overline{2}0{>}_{{\text{Ce}}_{\text{2}}{\text{O}}_{\text{2}}\text{S}}$	3.50	SS-SS	${\left\{110\right\}}_{\delta \text{-Fe}}//{\left\{11\overline{2}0\right\}}_{{\text{Ce}}_{\text{2}}{\text{O}}_{\text{2}}\text{S}}$	3.47
$<100{>}_{\delta \text{-Fe}}//<\overline{1}101{>}_{{\text{Ce}}_{\text{2}}{\text{O}}_{\text{2}}\text{S}}$	9.92	SS-PS

The computed results in Table 4 indicate that the mismatch degrees of atomic spacing and lattice plane spacing between δ-Ferrite and La₂O₂S, as well as Ce₂O₂S, along the close-packed crystallographic direction and close-packed planes, were both below 10%. These values satisfy the empirical criterion of the E2EM model.⁴⁷⁾ However, the mismatch degrees of atomic spacing along the close-packed direction between δ-Ferrite and LaAlO₃, CeAlO₃ do not satisfy the empirical criterion of the E2EM model. This suggests a reduced likelihood of δ-Ferrite nucleating with LaAlO₃ and CeAlO₃ as the core during the solidification process. In summary, the computational results of the E2EM model indicate that (La, Ce)₂O₂S can effectively act as a nucleation core for δ-Ferrite, resulting in the refinement of the solidification microstructure. Moreover, according to the criteria of the E2EM model, the establishment of potential orientation relationships between the δ-Ferrite and the rare earth inclusions should meet the following conditions: the matching crystallographic direction must lie on the matching lattice planes, and the matching of straight atomic rows should occur between straight atomic rows, while the matching of Z-type atomic rows should occur between Z-type atomic rows. Based on these criteria, a rough prediction can be made regarding the orientation relationship between δ-Ferrite and La₂O₂S, Ce₂O₂S. The rough predicted orientation relationship between δ-Ferrite and La₂O₂S is as follows:

  

$${[\overline{1}101]}_{\mathrm{L}{\mathrm{a}}_{\text{2}}{\mathrm{O}}_{\text{2}}\mathrm{S}}//{[100]}_{\delta \text{-}\mathrm{F}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}},\mathrm{\hspace{0.17em} }{(11\overline{2}0)}_{{\text{La}}_{\text{2}}{\text{O}}_{\text{2}}\text{S}}//{(011)}_{\delta \text{-Ferrite}}.$$

The rough predicted orientation relationship between δ-Ferrite and Ce₂O₂S is as follows:

  

$${[\overline{1}101]}_{\mathrm{C}{\mathrm{e}}_{\text{2}}{\text{O}}_{\text{2}}\text{S}}//{[100]}_{\delta \text{-}\mathrm{F}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}},\mathrm{\hspace{0.17em} }{(11\overline{2}0)}_{{\text{Ce}}_{\text{2}}{\text{O}}_{\text{2}}\text{S}}//{(0\overline{1}\overline{1})}_{\delta \text{-Ferrite}}.$$

Synthesize the above research results, it is reasonable to conclude that the primary mechanism driving the refinement of billet solidification microstructure involves the heterogeneous nucleation facilitated by rare earth inclusions. Figure 10 illustrates the heterogeneous nucleation process of δ-Ferrite with rare earth inclusions (La, Ce)₂O₂S as the core. Before δ-Ferrite solidifies, a considerable quantity of (La, Ce)₂O₂S has already formed in the molten steel. Due to the small mismatch between (La, Ce)₂O₂S and the δ-Ferrite interface, (La, Ce)₂O₂S inclusions can effectively act as heterogeneous nucleation cores for δ-Ferrite during the solidification process, resulting in a noticeable refinement of equiaxed grains. Meanwhile, the numerical density of (La, Ce) ₂O₂S increases with the increase of rare earth content, which leads to the decrease of the average size of equiaxed grains in the casting billet.

Fig. 10. The heterogeneous nucleation process of δ-Ferrite with (La, Ce)₂O₂S as the core. (Online version in color.)

5. Conclusions

The effect of composite rare earth treatment on solidification structure was studied through a combination of inclusion detection, evaluation of solidification microstructure, and theoretical calculation. The main conclusions are listed as follows:

(1) As the rare earth content increases, the average size of equiaxed grains decreases, while the change in the columnar grain ratio is relatively minor. The columnar grain rate in the casting billet was primarily affected by parameters such as casting speed during the continuous casting process.

(2) The results of inclusions detection using scanning electron microscopy (SEM) and statistical analysis with the ASPEX automatic inclusion analysis system revealed a formation sequence of stable inclusions when the rare earth content ranged from 0 wt% to 0.0058 wt%. The sequence was identified as Al₂O₃→(La, Ce)AlO₃→(La, Ce)₂O₂S, and the content of (La, Ce)₂O₂S increased continuously with the increment of rare earth content. The thermodynamic calculations obtained through Factsage8.2 reveal that at rare earth content levels of 0.0021 wt%, 0.0034 wt%, and 0.0058 wt%, the stable inclusion phases correspond to (La,Ce)AlO₃, a combination of (La,Ce)AlO₃ and (La,Ce)₂O₂S, and (La,Ce)₂O₂S, respectively.

(3) As the rare earth content increases, the content of Al₂O₃ inclusions and their pinning force on the equiaxed crystal grains initially decreases and then increases. Meanwhile, the concentration of rare earth inclusions and their pinning impact upon the equiaxed crystals experience distinct escalation, whereas the content of MnS inclusions and their pinning effect upon the equiaxed crystals exhibit a diminishing tendency. However, the effect of rare earth on the pinning force of inclusions was marginal.

(4) Thermodynamic calculation indicated that Ce addition had negligible effect on the equilibrium partition coefficient of Si, Al and Mn. Combined with the calculation results of GRF model, it is reasonable to consider that the contribution of rare earth element to the refinement of equiaxed crystals can be ignored.

(5) The outcomes obtained from the E2EM model calculations revealed that the principal mechanism responsible for the refinement of equiaxed crystals through rare earth treatment can be attributed to the heterogeneous nucleation effect of (La, Ce)₂O₂S.

Acknowledgements

This work was supported by the Jiangxi Province Major Scientific and Technological Research and Development Special Funding Project (No.20213AAE01009).

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